Wired Magazine has published several important articles on the
way deep laws of mathematics drive physics and biology.
The most recent, July 28, is by Matalie Wolchover, and is
titled “The Peculiar Math that Could Underly the Laws of Nature”. It’s also in Quanta Magazine here.
She is a mathematician from Waterloo University in Ontario,
and has worked with Penn State on this issue.
Her argument reminds me of the progression to real variables
to complex variable in graduate school in mathematics (in my case, at Kansas University
in the 1960s). Complex gives us some beauty, like the Mandelbrot set; and Liousville Theorem may explain why the Universe
seems infinite from any point.
From complex variables you get to quaternions, and from
those to octonions.
Now quaternion field theory doesn’t follow the commutative
law, and octernions don’t even follow the associate law. I remember giving my students quiz questions
on those laws when I worked as a graduate student assistant instructor (many of
them couldn’t restate the concepts).
From octonion math you can deduce string theory, the 11
dimensions and why time behaves the way it does. You can also explain the fundamental forces
in physics, maybe, and build quarks.
I hope you can’t build a contagious strangelet to make gray
goo.
I could wonder, though, wouldn’t these tuples behave like
vector spaces? Remember linear independence?
Here are a couple other big Wired (paywall) stories on theoretical mathematics.
John Rennie on July1, 2018 writes “This Mutation Math Shows How Life Keeps on Evolving.”
And on Dec. 17, 2017, Kevin Hartnett published, “Secret Link Discovered Between Pure Math and Physics” , the work of Minhyong Kim at the
University of Oxford, getting into “series of spaces”.
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